Menarche and E

Age at menarche on the population-level

Approach 1: Mean + 2SD

Adapting methods described in the poster uploaded on Google Drive, I first calculated the mean pre-pubertal fE2 concentration. Because infants/juvs have elevated fE2 when nursing, we need to exclude these individuals when determining what typical pre-pubertal fE2 looks like.

Per Slack communication on 7/17: defining prebuteral E from individuals greater than 2.5 years (def not nursing) and under 3 (def not pubertal)

Step 1: Preparing dataset of prepubertal individuals (2.5-3 yo)

## calculating average pre-pubertal E2 
prepubertal_data<-e_data |> 
  filter(age_at_sample >= 2.5 & age_at_sample <= 3) |>  # we want age 2.5-3...def pre menstruation
  select(ind_id, age_at_sample, e_conc_ug)

Step 2: Calculating average prepubertal E

prepubertal_e_data <- prepubertal_data |> 
   summarise(mean_e_conc_ug = mean(e_conc_ug, na.rm = TRUE),
            sd_e_conc_ug = sd(e_conc_ug, na.rm = TRUE)) 

mean_prepubertal_e_conc_ug <- prepubertal_e_data$mean_e_conc_ug
sd_prepubertal_e_conc_ug <- prepubertal_e_data$sd_e_conc_ug

Step 3: Calculating pubertal threshold E

Using the mean + 2SD approach:

calculated_treshold <- mean_prepubertal_e_conc_ug + 2*sd_prepubertal_e_conc_ug

print(paste("Calculated fE2 threshold for menarche: ", calculated_treshold, " ug/g"))
## [1] "Calculated fE2 threshold for menarche:  0.784032497466729  ug/g"

Step 4: Calculating population average age at menarche based on threshold E

Looking at the average age at which the population has an E reading that crosses the threshold E. Restricting dataset to individuals >3 years old.

## creating df ----
e_data_age_at_menarche_df <- e_data |>
  select(c(age_at_sample, age_at_sample_years, e_conc_ug)) |>
  group_by(age_at_sample) |>
  mutate(mean_e_at_age = mean(e_conc_ug, na.rm = TRUE),
         se_e_at_age = sd(e_conc_ug, na.rm = TRUE) / sqrt(n())) |>
  ungroup() |>
  arrange(age_at_sample) |>
  distinct() |> 
  group_by(age_at_sample_years) |>
  mutate(mean_e_at_age_years = mean(e_conc_ug, na.rm = TRUE),
         se_e_at_age_years = sd(e_conc_ug, na.rm = TRUE) / sqrt(n())) |>
  ungroup() |>
  select(-e_conc_ug) |>
  arrange(age_at_sample_years) |>
  distinct() 

## average_age_at_menarche----
average_age_at_menarche <- e_data_age_at_menarche_df |> 
  filter(age_at_sample > 3) |> 
  filter(mean_e_at_age > calculated_treshold) |> 
  slice(1) |> 
  pull(age_at_sample)


# standard error of average_age_at_menarche
se_age_at_menarche <- e_data_age_at_menarche_df |> 
  filter(age_at_sample > 3) |> 
  filter(mean_e_at_age > calculated_treshold) |> 
  summarise(se_age_at_sample = sd(age_at_sample, na.rm = TRUE) / sqrt(n())) |> 
  pull(se_age_at_sample)


print(paste("Calculated average age at menarche: ", average_age_at_menarche, " years"))
## [1] "Calculated average age at menarche:  3.22  years"
print(paste("SE average age at menarche: ", se_age_at_menarche))
## [1] "SE average age at menarche:  0.343412350546469"

NOTE: This calculated age is definitely too young.

Step 5: Trying (and failing) to get normality

The E data is super not normal at the population-level, even after attempting log transformation….I am holding off on any real modeling for now

shapiro.test(e_data_age_at_menarche_df$mean_e_at_age)
## 
##  Shapiro-Wilk normality test
## 
## data:  e_data_age_at_menarche_df$mean_e_at_age
## W = 0.20031, p-value < 2.2e-16
shapiro.test(log(e_data_age_at_menarche_df$mean_e_at_age))
## 
##  Shapiro-Wilk normality test
## 
## data:  log(e_data_age_at_menarche_df$mean_e_at_age)
## W = 0.99535, p-value = 0.008119

Plot of fE2 as a function of age: population-level

For interpretability, this plot just has the data sorted into age-years, rather than exact age estimations with lots of decimals

## get sample size ----
n_figure_1 <- nrow(e_data)

##Figure 1
par(mfrow = c(1,1))

ggplot(data = e_data_age_at_menarche_df |> 
         select(age_at_sample_years, mean_e_at_age_years, se_e_at_age_years) |> 
         distinct(), aes(x = age_at_sample_years, y = mean_e_at_age_years)) + 
  geom_smooth() + 
  geom_point()+
  geom_vline(xintercept = average_age_at_menarche, linetype = "dashed", color = "red") +
  geom_hline(yintercept = calculated_treshold, linetype = "dashed", color = "skyblue") +
  geom_errorbar(aes(ymin = mean_e_at_age_years - se_e_at_age_years, ymax = mean_e_at_age_years + se_e_at_age_years), width = 0.2) +
  geom_rect(aes(xmin = average_age_at_menarche - 1.96*se_age_at_menarche, xmax = average_age_at_menarche + 1.96*se_age_at_menarche, 
                ymin = -Inf, ymax = Inf), alpha = 0.05, fill = "pink") +
  ggtitle(paste0("Average estradiol by age at sample (N = ", n_figure_1, " samples)"))+
  xlab("Age at sample")+
  ylab("Fecal estradiol (ug/g)")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

Interpreting the graph:

  • The black circles and error bars represent the average age fE2 reading (with standard error) for each age-year for the population

  • The blue line represents the results of a Loess regression, a non-parametric approach to modeling the relationship between x and y. The gray shading around the blue line is the error of the estimate.

  • The dashed light blue line is the calculated prepubertal fE threshold (y = 0.7840325 ug/g)

  • The dashed red line is the calculated average age at puberty (x = 3.22 years)

  • The shaded area around the dashed red line is the 95% CI for the average age at puberty estimate (3.22 ± 1.96* SE)

Age at menarche on the individual-level

Plot of fE2 as a function of age: individual-level

NOTE: I haven’t yet calculated individual E thresholds/ages at menarche because I think we are going to want a different approach than mean + 2sd….still working on that.

I am pulling data on females that we have good E coverage for before and after potential menarche…I’m looking for IDs with samples starting at least by age 3. At least 25 samples per ID. That leaves us with the following:

par(mfrow = c(1,1))

# Panel of all individual females who have good E coverage before and after menarche
females_for_menarche_panel<-e_data |> 
  group_by(ind_id) |> 
  filter(min(age_at_sample)<3) |>
  mutate(count = n()) |> 
  ungroup() |> 
  select(ind_id,count) |> 
  arrange(desc(count)) |> 
  distinct() |> 
  filter(count>25) |> 
  pull(ind_id)

females_for_menarche_panel_df<- e_data |> 
  filter(ind_id %in% females_for_menarche_panel) |>
  filter(age_at_sample < 8) |>
  select(ind_id, age_at_sample, sample_id, date, month, time, hour, e_conc_ug, is_pregnant) |> 
  arrange(ind_id, age_at_sample) |> 
  mutate(date = as.Date(date))

n_figure_2 <-nrow(females_for_menarche_panel_df)

# facet wrap plots with geom_smooth
ggplot(data = females_for_menarche_panel_df, aes(x = age_at_sample, y = log(e_conc_ug), color = ind_id)) +
  geom_point()+
  facet_wrap(~ ind_id)+
  geom_smooth()+
  ggtitle(paste0("Estradiol by age at sample, separated by individual (n = ", n_figure_2, " samples)"))+
  xlab("Age at sample")+
  ylab("Log-transformed fecal estradiol (log(ug/g))")+
  theme(legend.position = "none")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

# Loop through each individual and create a ggplot for each
for (individual in females_for_menarche_panel) {
  individual_data <- females_for_menarche_panel_df |> filter(ind_id == individual)
  
  p <- ggplot(data = individual_data, aes(x = age_at_sample, y = log(e_conc_ug))) +
    geom_point() +
    ggtitle(paste0("Estradiol by age at sample for individual ", individual, " (n = ", nrow(individual_data), " samples)")) +
    xlab("Age at sample") +
    ylab("Log-transformed fecal estradiol (log(ug/g))") +
    theme(legend.position = "none")+
    geom_line(color = "blue")
  print(p)
}

^Note that the y-axis is log-transformed on this plot

Modeling E and age

Step 1. Assessing normality

shapiro.test(females_for_menarche_panel_df$e_conc_ug) #nope
## 
##  Shapiro-Wilk normality test
## 
## data:  females_for_menarche_panel_df$e_conc_ug
## W = 0.46254, p-value < 2.2e-16
shapiro.test(log(females_for_menarche_panel_df$e_conc_ug)) # log transformation does the trick!
## 
##  Shapiro-Wilk normality test
## 
## data:  log(females_for_menarche_panel_df$e_conc_ug)
## W = 0.99592, p-value = 0.1774

Log transformation does the trick! Data is now normal for our young female panel.

Step 2. Modeling E2 and age

I am including individual ID as a random effect. In unadjusted model, fixed effects are month and time of day (accounting for seasonality and diurnal variation) with individual ID included as a random effect. Any other things to control for?

The adjusted model includes age as a fixed effect. Age improves the model fit!

unadjusted_e_model <- lmer(log(e_conc_ug) ~  + month + hour+ (1 | ind_id), data = females_for_menarche_panel_df)

adjusted_e_model <- lmer(log(e_conc_ug) ~ age_at_sample + month + hour+ (1 | ind_id), data = females_for_menarche_panel_df)

anova(unadjusted_e_model, adjusted_e_model) # adjusted_e_model fits better
## refitting model(s) with ML (instead of REML)
## Data: females_for_menarche_panel_df
## Models:
## unadjusted_e_model: log(e_conc_ug) ~ +month + hour + (1 | ind_id)
## adjusted_e_model: log(e_conc_ug) ~ age_at_sample + month + hour + (1 | ind_id)
##                    npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)    
## unadjusted_e_model    5 1879.4 1900.8 -934.70   1869.4                         
## adjusted_e_model      6 1751.7 1777.5 -869.86   1739.7 129.68  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(adjusted_e_model)
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(e_conc_ug) ~ age_at_sample + month + hour + (1 | ind_id)
##    Data: females_for_menarche_panel_df
## 
## REML criterion at convergence: 1758.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.16124 -0.62234  0.00391  0.65935  2.72881 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ind_id   (Intercept) 0.150    0.3874  
##  Residual             1.461    1.2087  
## Number of obs: 537, groups:  ind_id, 8
## 
## Fixed effects:
##               Estimate Std. Error t value
## (Intercept)   -2.78282    0.32894  -8.460
## age_at_sample  0.50977    0.04226  12.062
## month          0.08792    0.01492   5.894
## hour          -0.04200    0.01934  -2.171
## 
## Correlation of Fixed Effects:
##             (Intr) ag_t_s month 
## age_at_smpl -0.581              
## month       -0.257  0.022       
## hour        -0.616 -0.018 -0.031
#checking for multicollinearity -- low (~ 1)
vif(adjusted_e_model)
## age_at_sample         month          hour 
##      1.000802      1.001467      1.001289
print("No multicollinearity -- yay!")
## [1] "No multicollinearity -- yay!"

Step 3. Checking model diagnostics

Tldr: model passes diagnostics—yay

# checking model diagnostics
plot(adjusted_e_model) #resids vs leverage -- pretty good

lattice::qqmath(adjusted_e_model) ## qq norm plot -- good

plot(adjusted_e_model, # scale location plot -- pretty good
     sqrt(abs(resid(.)))~fitted(.),
     type=c("p","smooth"), col.line=1)

Menarche and Duck Face

NOTE: I am holding off on reporting on this until we have the updated behavioral data containing group scan observations of duck face….planning to adapt methods from Sen et al. 2022

Cycling E

NOTE: I am holding off on reporting on this until we have the updated behavioral data containing group scan observations of duck face….planning to adapt methods from Sen et al. 2022

par(mfrow = c(1,1))

# Panel of all individual females who have good E coverage before and after menarche
females_for_cycling_panel<-e_data |> 
  group_by(ind_id) |> 
  filter(min(age_at_sample)>3) |> 
  mutate(count = n()) |> 
  ungroup() |> 
  select(ind_id,count) |> 
  arrange(desc(count)) |> 
  distinct() |> 
  filter(count>25) |> 
  pull(ind_id)

females_for_cycling_panel_df<- e_data |> 
  filter(ind_id %in% females_for_cycling_panel) |>
  mutate(date = as.Date(date)) |> 
  filter(date > as.Date("2021-12-31")) |> 
  select(ind_id, age_at_sample, sample_id, date, month, time, hour, e_conc_ug, is_pregnant) |> 
  arrange(ind_id, age_at_sample) 
n_figure_2 <-nrow(females_for_cycling_panel_df)

create_continuous_segments <- function(df) {
  df %>%
    arrange(date) %>%
    mutate(segment = cumsum(is_pregnant == "P") + 1) %>%
    group_by(segment) %>%
    filter(any(is_pregnant == "NP")) %>%
    ungroup() %>%
    mutate(segment = cumsum(is_pregnant == "P") + 1) %>%
    filter(is_pregnant == "NP")
}


# Loop through each individual and create a ggplot for each
for (individual in females_for_cycling_panel) {
  individual_data <- females_for_cycling_panel_df |> filter(ind_id == individual)
  
  # Create continuous segments based on NP periods
  segmented_data <- create_continuous_segments(individual_data)
  
  p <- ggplot(data = individual_data, aes(x = date, y = log(e_conc_ug))) +
    geom_point(aes(color = is_pregnant)) +
    ggtitle(paste0("Estradiol by age at sample for individual ", individual, " (n = ", nrow(individual_data), " samples)")) +
    xlab("Date") +
    ylab("Log-transformed fecal estradiol (log(ug/g))") +
    theme(legend.position = "none") +
    geom_line(data = segmented_data, aes(group = segment), color = "blue")  # Plot lines for continuous NP segments
  
  print(p)
}

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

Pregnancy E

Age at first birth

Could you please share the estimated/confirmed ages of all of our IDs? I can’t really assign this easily (unless I work backwards from age at sample info….). I know I had made a Google Sheet at some point with this information, but I no longer have access. Thanks!

Assigning gestation lengths

Haven’t looked into this yet…stay tuned.

E across trimesters

QUESTION: I see some individuals are marekd as pregnant (e..g, is_pregnant = “P”), but the preg_trim column is blank. What do I do about this?

For now, I’m excluding pregnant individuals with missing trimester info.

Step 1. Preparing dataset for pregnant individuals with known trimester info

pregnant_df<-e_data |> 
  select(ind_id, month, hour, age_at_sample, e_conc_ug, preg_trim, pregnancy_num, is_pregnant) |> 
  filter(is_pregnant == "P") |> 
  filter(preg_trim !="")

n_pregnant_df <- nrow(pregnant_df)

Step 2. Data visualization

Note: y-axis is log-transformed

par(mfrow = c(1,1))
ggplot(data = pregnant_df, aes(x = preg_trim, y = log(e_conc_ug)))+
  geom_boxplot()+
  geom_jitter(alpha = 0.1)+
  ggtitle(paste("Estradiol and gestation (N = ", n_pregnant_df, "samples)")) +
  xlab("Pregnancy trimester")+
  ylab("Log-transformed fecal estradiol (log(ug/g))")

Step 3. Assessing normality

Data is normal following log transformation

shapiro.test(pregnant_df$e_conc_ug)
## 
##  Shapiro-Wilk normality test
## 
## data:  pregnant_df$e_conc_ug
## W = 0.33877, p-value < 2.2e-16
shapiro.test(log(pregnant_df$e_conc_ug))
## 
##  Shapiro-Wilk normality test
## 
## data:  log(pregnant_df$e_conc_ug)
## W = 0.99539, p-value = 0.6763

Step 4. ANOVA and Tukey’s HSD

Among trimesters, we only see that T2 is significantly lower than T3; no significant difference between T1-T2 or T1-T3.

anova_result_pregancy_e <- aov(log(e_conc_ug) ~ preg_trim, data = pregnant_df)

summary(anova_result_pregancy_e)
##              Df Sum Sq Mean Sq F value  Pr(>F)   
## preg_trim     2   17.7   8.853   5.964 0.00296 **
## Residuals   242  359.2   1.484                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tukey_results_pregnancy_e <- TukeyHSD(anova_result_pregancy_e)
print(tukey_results_pregnancy_e)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = log(e_conc_ug) ~ preg_trim, data = pregnant_df)
## 
## $preg_trim
##             diff        lwr       upr     p adj
## T2-T1 -0.3732333 -0.8473855 0.1009188 0.1537996
## T3-T1  0.2486747 -0.2191212 0.7164707 0.4229352
## T3-T2  0.6219081  0.1957494 1.0480667 0.0019638

Step 5: Modeling E2 across pregnancy

## what other control variables should I include?
unadjusted_pregnancy_model <- lmer(log(e_conc_ug) ~ age_at_sample + month+ hour+ (1 | ind_id), data = pregnant_df)

adjusted_pregnancy_model <- lmer(log(e_conc_ug) ~ age_at_sample + month + hour+preg_trim + (1 | ind_id), data = pregnant_df)

anova(unadjusted_pregnancy_model, adjusted_pregnancy_model) # adjusted model is better fit--pregnancy predicts E
## refitting model(s) with ML (instead of REML)
## Data: pregnant_df
## Models:
## unadjusted_pregnancy_model: log(e_conc_ug) ~ age_at_sample + month + hour + (1 | ind_id)
## adjusted_pregnancy_model: log(e_conc_ug) ~ age_at_sample + month + hour + preg_trim + (1 | ind_id)
##                            npar    AIC    BIC  logLik deviance  Chisq Df
## unadjusted_pregnancy_model    6 784.51 805.52 -386.25   772.51          
## adjusted_pregnancy_model      8 775.48 803.49 -379.74   759.48 13.024  2
##                            Pr(>Chisq)   
## unadjusted_pregnancy_model              
## adjusted_pregnancy_model     0.001486 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(adjusted_pregnancy_model)
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(e_conc_ug) ~ age_at_sample + month + hour + preg_trim + (1 |  
##     ind_id)
##    Data: pregnant_df
## 
## REML criterion at convergence: 781.5
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.74934 -0.62059  0.01613  0.67608  3.01420 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ind_id   (Intercept) 0.4587   0.6773  
##  Residual             1.1646   1.0792  
## Number of obs: 245, groups:  ind_id, 23
## 
## Fixed effects:
##               Estimate Std. Error t value
## (Intercept)    1.78746    0.52446   3.408
## age_at_sample  0.01562    0.02276   0.686
## month          0.02944    0.02363   1.246
## hour          -0.07165    0.02894  -2.476
## preg_trimT2   -0.17724    0.20993  -0.844
## preg_trimT3    0.41154    0.19692   2.090
## 
## Correlation of Fixed Effects:
##             (Intr) ag_t_s month  hour   prg_T2
## age_at_smpl -0.538                            
## month       -0.372 -0.015                     
## hour        -0.655  0.008  0.030              
## preg_trimT2 -0.293 -0.080  0.452 -0.019       
## preg_trimT3 -0.311 -0.017  0.403 -0.019  0.660

Step 6: Checking model diagnostics

Tldr: model passes diagnostics—yay

#checking for multicollinearity -- low (~ 1)
vif(adjusted_pregnancy_model)
##                   GVIF Df GVIF^(1/(2*Df))
## age_at_sample 1.009100  1        1.004540
## month         1.291221  1        1.136319
## hour          1.002459  1        1.001229
## preg_trim     1.301658  2        1.068130
# checking model diagnostics
plot(adjusted_pregnancy_model) #resids vs leverage -- good

lattice::qqmath(adjusted_pregnancy_model) ## qq norm plot -- good...small tail on right

plot(adjusted_pregnancy_model, # scale location plot -- good
     sqrt(abs(resid(.)))~fitted(.),
     type=c("p","smooth"), col.line=1)

Lactation E 

Step 1. Preparing dataset for lactating vs not lactating

Only looking at adults (ages >6)

lactation_df <- e_data |> 
  select(ind_id, month, hour, age_at_sample, e_conc_ug, lactating) |> 
  filter(age_at_sample > 6)

n_lactation_df<-nrow(lactation_df)

Step 2. Data visualization

Note: y-axis is log-transformed

ggplot(data = lactation_df, aes(x = lactating, y = log(e_conc_ug)))+
  geom_boxplot()+
  geom_jitter(alpha = 0.1)+
  ggtitle(paste("Estradiol and lactation (N = ", n_pregnant_df, "samples)")) +
  xlab("Lactating")+
  ylab("Log-transformed fecal estradiol (log(ug/g))")

Step 3. Assessing normality

Data is still not normal following log transformation

shapiro.test(lactation_df$e_conc_ug)
## 
##  Shapiro-Wilk normality test
## 
## data:  lactation_df$e_conc_ug
## W = 0.26856, p-value < 2.2e-16
shapiro.test(log(lactation_df$e_conc_ug))
## 
##  Shapiro-Wilk normality test
## 
## data:  log(lactation_df$e_conc_ug)
## W = 0.99144, p-value = 6.802e-05

Step 4. Mann Whitney U Test

Data is not normal, so can’t do ANOVA. Let’s use a nonparametric approach to see if E is significantly lower during lactation….it is (W = 98014, p < 0.001)

wilcox.test(log(e_conc_ug) ~ lactating, data = lactation_df)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  log(e_conc_ug) by lactating
## W = 98014, p-value = 5.847e-09
## alternative hypothesis: true location shift is not equal to 0

Step 5. Modeling E2 and lactation

Technically, data should be normal for this. BUT I think our sample might be large enough that we’re okay violating this assumption?

## what other control variables should I include?
unadjusted_lactation_model <- lmer(log(e_conc_ug) ~ age_at_sample + month+ hour + (1 | ind_id), data = e_data)

adjusted_lactation_model <- lmer(log(e_conc_ug) ~ age_at_sample + month+ hour + lactating + (1 | ind_id), data = e_data)

anova(unadjusted_lactation_model,adjusted_lactation_model) # adjusted model is better fit--lactation predicts E
## refitting model(s) with ML (instead of REML)
## Data: e_data
## Models:
## unadjusted_lactation_model: log(e_conc_ug) ~ age_at_sample + month + hour + (1 | ind_id)
## adjusted_lactation_model: log(e_conc_ug) ~ age_at_sample + month + hour + lactating + (1 | ind_id)
##                            npar    AIC    BIC  logLik deviance  Chisq Df
## unadjusted_lactation_model    6 4843.2 4874.7 -2415.6   4831.2          
## adjusted_lactation_model      7 4803.3 4840.0 -2394.6   4789.3 41.974  1
##                            Pr(>Chisq)    
## unadjusted_lactation_model               
## adjusted_lactation_model     9.25e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(adjusted_lactation_model) # lactation = lower E
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(e_conc_ug) ~ age_at_sample + month + hour + lactating + (1 |  
##     ind_id)
##    Data: e_data
## 
## REML criterion at convergence: 4813.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1108 -0.6274 -0.0233  0.6412  3.3238 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ind_id   (Intercept) 2.147    1.465   
##  Residual             1.626    1.275   
## Number of obs: 1403, groups:  ind_id, 44
## 
## Fixed effects:
##                Estimate Std. Error t value
## (Intercept)   -1.633063   0.349677  -4.670
## age_at_sample  0.173253   0.020625   8.400
## month          0.061315   0.009774   6.273
## hour          -0.022011   0.012923  -1.703
## lactatingYES  -0.635455   0.094448  -6.728
## 
## Correlation of Fixed Effects:
##             (Intr) ag_t_s month  hour  
## age_at_smpl -0.587                     
## month       -0.188  0.038              
## hour        -0.426  0.007  0.032       
## lactatngYES  0.058 -0.182 -0.047  0.040

Step 6. Checking model diagnostics

Tldr: model passes diagnostics—yay

#checking for multicollinearity -- low (~ 1)
vif(adjusted_lactation_model)
## age_at_sample         month          hour     lactating 
##      1.035517      1.004192      1.002907      1.038010
# checking model diagnostics
plot(adjusted_lactation_model) #resids vs leverage -- good

lattice::qqmath(adjusted_lactation_model) ## qq norm plot -- good...small tail on right

plot(adjusted_lactation_model, # scale location plot -- good
     sqrt(abs(resid(.)))~fitted(.),
     type=c("p","smooth"), col.line=1)

Male takeovers and E

Can I please have access to these data?